Talk:Statistical distance

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Comparison table

Would be nice to have a comparison table to see how far the distance or divergence measures are from being a metric. Please feel free to fill in missing (-) data, references being welcome too. I mostly copied data from the articles of these distances:

Divergence between distributions	Symmetric	Nonnegative	Triangle inequality	Identity of indiscernibles	Metric
Kullback–Leibler divergence	no	yes	no	yes	no
Hellinger distance	-	yes	-	-	-
Total variation distance of probability measures	yes	yes	yes	yes	yes
Jensen–Shannon divergence	yes	-	-	-	no
Jensen–Shannon distance	yes	yes	yes	yes	yes
Lévy–Prokhorov metric	yes	yes	yes	yes	yes
Bhattacharyya distance	-	-	-	-	no
Wasserstein metric	yes	yes	yes	yes	yes

Divergence between a point and a distribution	Symmetric	Nonnegative	Triangle inequality	Identity of indiscernibles	Metric
Mahalanobis distance	-	-	-	-	-

Olli Niemitalo (talk) 10:22, 3 December 2014 (UTC)[reply]

That's nice. I've completed missing entries on the total variation distance. - Saibod (talk) 23:54, 3 March 2016 (UTC)[reply]

There is no mention of the statistical distance used in 100% of the crypto papers I've encountered. SD(u,v) = 1/2 ∑ |v_i - u_i| . Is there a reason for that, or is it just missing? For example "Three XOR-Lemmas -- An Exposition, Oded Goldreich" states it. "Randomness Extraction and Key Derivation Using the CBC, Cascade and HMAC Modes, Yevgeniy Dodis, Rosario Gennaro, Johan Hastad, Hugo Krawczyk4 and Tal Rabin" states the same definition. Those are the first two papers I checked.

David in oregon (talk) 05:08, 1 October 2016 (UTC)[reply]

Never mind. It was a special case of the total variation distance. David in oregon (talk) 23:27, 1 October 2016 (UTC)[reply]